At what altitude will the acceleration due to gravity be `25%` of that at the earth's surface (given radius of earth is `R`)?

Options

A. R
B. `(3)/(8)R`
C. `( R)/(2)`
D. `(1)/(4)R`

Answer

A

Explanation

`(g')/(g)=((R )/(R+h))^(2) " " therefore (1)/(4)=((R )/(R+h))^(2)`
`therefore (1)/(2)=(R )/(R+h)`
`therefore R+h=2R " " therefore h = R`